In his Ph.D. thesis [1]}, Bedi computed the cohomology of some of the twisting sheaves \((d)\)  on projectivoid space. His proof was modeled on the computation for classical projective space in Ravi Vakil's algebraic geometry notes ([2]} Chapter 18.2), but doesn't explicitly take into account the completions involved, and only includes the case for \(n=2\) . Instead, we adapt the proof from EGA III [3]} which relates Čech cohomology to the Koszul complex. We also fill in the result, computing the cohomology of every line bundle in every degree. Our rings are going to be topologically \([1/p]\)  graded, and for a graded ring \(A\)  we will denote by \(A_d\)  the degree \(d\)  part.

Let \(X = ^{n,}\)  be projectivoid space, and \(_X(d)\in X\)  an arbitrary line bundle. Then:
